Properties

Label 3.4.ag_v_abz
Base Field $\F_{2^2}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $3$
Weil polynomial:  $1 - 6 x + 21 x^{2} - 51 x^{3} + 84 x^{4} - 96 x^{5} + 64 x^{6}$
Frobenius angles:  $\pm0.0783669125587$, $\pm0.364419459234$, $\pm0.462679369643$
Angle rank:  $3$ (numerical)
Number field:  6.0.1305639.1
Galois group:  $A_4\times C_2$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 17 5491 301121 14282091 964160117 68375244349 4470803778248 283155607880811 18040389558202421 1154563260050537461

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 23 74 215 914 4076 16652 65927 262523 1050068

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.